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<title>The MPL Reference Manual: Metafunction</title>
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<div class="section" id="metafunction">
<h1><a class="toc-backref" href="./metafunctions-concepts.html#id1512">Metafunction</a></h1>
<div class="section" id="id822">
<h3><a class="subsection-title" href="#description" name="description">Description</a></h3>
<p id="nullary-metafunction">A <em>metafunction</em> is a class or a class template that represents a
function invocable at compile-time. An non-nullary metafunction is
invoked by instantiating the class template with particular
template parameters (metafunction arguments); the result of the
metafunction application is accessible through the instantiation's
nested <tt class="literal"><span class="pre">type</span></tt> typedef. All metafunction's arguments must be types
(i.e. only <em>type template parameters</em> are allowed). A metafunction
can have a variable number of parameters. A <em>nullary metafunction</em> is
represented as a (template) class with a nested <tt class="literal"><span class="pre">type</span></tt> typename
member.</p>
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<div class="section" id="id823">
<h3><a class="subsection-title" href="#expression-requirements" name="expression-requirements">Expression requirements</a></h3>
<p>In the following table and subsequent specifications, <tt class="literal"><span class="pre">f</span></tt> is a <a class="reference internal" href="./metafunction.html">Metafunction</a>.</p>
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<tr><th class="head">Expression</th>
<th class="head">Type</th>
<th class="head">Complexity</th>
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<tr><td><tt class="literal"><span class="pre">f::type</span></tt></td>
<td>Any type</td>
<td>Unspecified.</td>
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<tr><td><tt class="literal"><span class="pre">f&lt;&gt;::type</span></tt></td>
<td>Any type</td>
<td>Unspecified.</td>
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<tr><td><tt class="literal"><span class="pre">f&lt;a1,..,an&gt;::type</span></tt></td>
<td>Any type</td>
<td>Unspecified.</td>
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<div class="section" id="id824">
<h3><a class="subsection-title" href="#expression-semantics" name="expression-semantics">Expression semantics</a></h3>
<pre class="literal-block">
typedef f::type x;
</pre>
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<tr class="field"><th class="field-name">Precondition:</th><td class="field-body"><tt class="literal"><span class="pre">f</span></tt> is a nullary <a class="reference internal" href="./metafunction.html">Metafunction</a>; <tt class="literal"><span class="pre">f::type</span></tt> is a <em>type-name</em>.</td>
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<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><tt class="literal"><span class="pre">x</span></tt> is the result of the metafunction invocation.</td>
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<pre class="literal-block">
typedef f&lt;&gt;::type x;
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<tr class="field"><th class="field-name">Precondition:</th><td class="field-body"><tt class="literal"><span class="pre">f</span></tt> is a nullary <a class="reference internal" href="./metafunction.html">Metafunction</a>; <tt class="literal"><span class="pre">f&lt;&gt;::type</span></tt> is a <em>type-name</em>.</td>
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<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><tt class="literal"><span class="pre">x</span></tt> is the result of the metafunction invocation.</td>
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<pre class="literal-block">
typedef f&lt;a1,<em>...</em> a<em>n</em>&gt;::type x;
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<tr class="field"><th class="field-name">Precondition:</th><td class="field-body"><tt class="literal"><span class="pre">f</span></tt> is an <em>n</em>-ary <a class="reference internal" href="./metafunction.html">Metafunction</a>; <tt class="literal"><span class="pre">a1</span></tt>,... <tt class="literal"><span class="pre">an</span></tt> are types;
<tt class="literal"><span class="pre">f&lt;a1,...an&gt;::type</span></tt> is a <em>type-name</em>.</td>
</tr>
<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><tt class="literal"><span class="pre">x</span></tt> is the result of the metafunction invocation
with the actual arguments <tt class="literal"><span class="pre">a1</span></tt>,... <tt class="literal"><span class="pre">an</span></tt>.</td>
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<div class="section" id="id825">
<h3><a class="subsection-title" href="#models" name="models">Models</a></h3>
<ul class="simple">
<li><a class="reference internal" href="./identity.html">identity</a></li>
<li><a class="reference internal" href="./plus.html">plus</a></li>
<li><a class="reference internal" href="./begin.html">begin</a></li>
<li><a class="reference internal" href="./insert.html">insert</a></li>
<li><a class="reference internal" href="./fold.html">fold</a></li>
</ul>
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<div class="section" id="id826">
<h3><a class="subsection-title" href="#see-also" name="see-also">See also</a></h3>
<p><a class="reference internal" href="./metafunctions.html">Metafunctions</a>, <a class="reference internal" href="./metafunction-class.html">Metafunction Class</a>, <a class="reference internal" href="./lambda-expression.html">Lambda Expression</a>, <a class="reference internal" href="./invocation.html">invocation</a>, <a class="reference internal" href="./apply.html">apply</a>, <a class="reference internal" href="./lambda.html">lambda</a>, <a class="reference internal" href="./bind.html">bind</a></p>
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